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Matrices and Determinants question

2016 · Shift 1 · Q35
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  2. /JEE Advanced
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  5. /2016 · Shift 1 · Q35

Matrices and Determinants question

2016 · Shift 1 · Q35

JEE AdvancedMathematicsMatrices and DeterminantsNumerical+3 / −1
Let z=−1+3i2z = {{ - 1 + \sqrt 3 i} \over 2}z=2−1+3​i​, where i=−1i = \sqrt { - 1}i=−1​, and r, s ∈\in∈{1, 2, 3}. Let P=[(−z)rz2sz2szr]P = \left[ {\begin{matrix} {{{( - z)}^r}} & {{z^{2s}}} \\ {{z^{2s}}} & {{z^r}} \\ \end{matrix} } \right]P=[(−z)rz2s​z2szr​] and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which P2 =−-− I is ‾\underline{\hspace{2cm}}​.
Numerical answer
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